A medical graft connector or plug is made, for example, by cutting end portions of a tube of highly elastic material axially at numerous locations spaced circumferentially around the tube to produce a plurality of fingers which extend axially from each end of an uncut medial portion of the tube. The fingers are deflected radially outwardly from the medial portion and set in that condition. For a graft connector, the medial portion is coaxially connected to an end portion of a tubular graft. The connector is then installed through an aperture in the side wall of a patients tubular body conduit, for example, by using a delivery tube in which the fingers are elastically deflected back to approximately their initial positions. When the delivery conduit is withdrawn from the connector, the fingers spring out to engage the inner and outer surfaces of the body conduit wall. For a plug, the medial portion is occluded and then the structure is installed through the aperture to be plugged in a manner similar to installation of the connector.
